A particle executing simple harmonic motion with amplitude has the same potential and kinetic energies at the displacement [2024]

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Solution

Q.
A particle executing simple harmonic motion with amplitude $A$ has the same potential and kinetic energies at the displacement [2024]

1 $2 \sqrt{A}$

2 $\frac{A}{2}$

3 $\frac{A}{\sqrt{2}}$

4 $A \sqrt{2}$

Ans.
(3)

Let the displacement of particle be $x$ .

Given, Kinetic energy = Potential energy

$\frac{1}{2} K (A^{2} - x^{2}) = \frac{1}{2} K x^{2}$

or $A^{2} - x^{2} = x^{2}$

or $A^{2} = 2 x^{2}$

$\Rightarrow x = \frac{A}{\sqrt{2}}$

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